The present invention relates generally to optics. More particularly, the invention provides techniques for correcting optical aberrations. Merely by way of example, the invention has been applied to optical mirrors, but it would be recognized that the invention has a much broader range of applicability.
Optical system has been widely used for detecting images of various targets. The optical system usually introduces discrepancies to the images. The discrepancies including phase errors result from various sources, such as aberrations associated with individual segments of optical system including optical mirrors and discrepancies between input and output of optical system. These errors often need to be estimated and corrected in order to improve image quality. For example, a space telescope such as the James Webb Space Telescope may have large phase errors after its deployment, and these aberrations often need to be corrected with the telescope remaining in space.
In order to correct the optical aberrations, a Green's function approach has been proposed. This method derives the transport of intensity equation and solves for the auxiliary function. In other words, the Green's function approach uses known phase or phase gradient at the boundary of optical aperture of the optical system and determines the phase map of the entire optical aperture. Applied to an astronomical telescope, this method measures irradiance on either side of telescope focus and radial gradient of wavefront at the edge of telescope aperture. Irradiance measurements do not need to be performed on planes symmetrically located on either side of telescope focus. Consequently, a Poisson equation is solved to obtain the wavefront error in the interior of the telescope aperture.
When the wavefront error of an aperture is large, the Green's function approach usually cannot effectively sample the entire optical aperture. Instead, the optical aperture is usually divided into several sub-apertures, and phases within each sub-aperture are measured. Phase errors in each sub-aperture are then determined and corrected. Afterwards, sizes of sub-apertures are increased, and phase errors within enlarged sub-apertures are further corrected. Through iterations, phase errors within the aperture become so small that the entire aperture may be sampled. This iterative sub-aperture approach requires additional masks and setups, and may even require several iterative corrections at each sub-aperture size. Hence this method is costly and time consuming.
In addition, the above method sometimes uses curvature-based wavefront sensing. This sensing technique requires information about radial derivative of phase at the boundary of optical aperture. For large mirrors with several segments, a large number of boundary radial derivatives need to be determined. Hence this method may be cumbersome.
FIG. 1 is a simplified diagram illustrating technique for phase error correction. The correction method includes at least five processes: secondary mirror alignment process 110, coarse tilt adjustment process 120, coarse petal figuring process 130, inter-petal phasing process 140, tilt/figure refinement process 150, and full aperture figuring process 160. Inter-petal phasing process 140 and tilt/figure refinement process 150 may be performed iteratively. As shown in FIG. 1, processes 110, 120, 130, and 140 use different pupil plane masks 112, 122, 132, 142, and 152 respectively. In addition, processes 110, 130, 150, and 160 use additional hardware. For example, process 110 uses Phase Diverse Phase Retrieval (“PDPR”) plates 114, process 130 uses fine steering mirror 134, process 150 uses PDPR plates 154 and fine steering mirror 155, and process 160 uses PDPR plates 164. At secondary mirror alignment process 110, point source functions (“PSFs”) in focal plane and defocus planes are measured, and sharpness maximization and PDPR analysis are performed. At coarse tilt adjustment process 120, PSFs for each petal is measured, and centroid analysis is performed. At coarse petal figuring process 130, PSFs for each sub-aperture is measured, and analysis based on PSF maximization algorithm is performed. At inter-petal phasing process 140, grism fringes are measured, and fringe analysis is performed. At tilt/figure refinement process 150, PSFs for each petal in focal plane and defocus planes are measured, and centroid analysis and PDPR analysis are performed. At full aperture figuring process 160, PSFs for entire aperture in focal plane and defocus planes are measured, and PDPR analysis is performed.
Hence it is desirable to simplify and improve phase correction technique.